De Morgan's Laws

De Morgan’s Laws explain how to negate logical quantifiers: negating a universal statement becomes an existential one, and vice versa. In formal terms, $\neg \forall x \ P(x)$ is equivalent to $\exists x \ \neg P(x)$, and $\neg \exists x \ P(x)$ is equivalent to $\forall x \ \neg P(x)$.

The rules for negating quantifiers can be summarised as: * $\neg \forall x \ P(x) \equiv \exists x \ \neg P(x)$ * $\neg \exists x \ P(x) \equiv \forall x \ \neg P(x)$